There are certainly easier pursuits out there, but it is indeed possible to make crystals using rocks as your starting material. We simply have to use chemical and physical approaches that somehow lead to crystal formation. Nature provides most crystals through one of two processes – precipitation or cooling. Precipitation occurs when water evaporates, leaving behind supersaturated solutions of minerals which are forced to leave solution, returning to their solid form. Cooling is common only with molten rock, as in lava flows, when the surrounding temperature is too low for the rock to remain liquid. In either case, nice crystals only form when the process occurs slowly.
To make a crystal from a rock using precipitation, we first must dissolve the rock. Most rocks don’t simply dissolve in water. (Rock salt will, but those are already salt crystals, so why bother?) Limestone and Marble will dissolve in acidified water, as many statues can testify after years of acid rain showers. Both are primarily calcium carbonate. Dissolving them in acid gives a solution of carbonic acid, along with calcium and whatever anion was a part of the original acid. Choose your acid for the crystal you desire. Hydrochloric acid (a.k.a. muriatic acid) will let you make calcium chloride crystals, for instance. To eliminate the carbonic acid, we exploit the property that carbonic acid is the same thing as carbon dioxide dissolved in water. Heat the solution nearly to boiling (we don’t really want to boil off the water) to render the carbon dioxide insoluble, and it leaves as a gas. You can speed the process by pulling a vacuum over the solution too, if you have access to vacuum that is. After a solid hour of heating, it’s a safe bet that the carbon dioxide is gone. Now you probably do want to reduce the amount of water, so keep heating to evaporate the liquid. (If you are paranoid about carbon dioxide returning to solution, you can keep the mixture under nitrogen.) Ideally, you’ll get down to where you have a saturated solution, though unless you’ve done the math from the start, a guess is your best bet. Then you just let the solution cool and sit. Over time, the crystals form. If you already have a seed crystal, you would add it to encourage growth.
Making a crystal by cooling is an unlikely project for home. This is done commercially in industry, making quartz crystals, for example. The basic procedure is simple enough – melt the material at high temperature and pressure, and then allow it to cool and reduce the pressure both slowly and at a controlled rate, preferably in the presence of a seed crystal. The engineering that is required to make this happen, however, is heavy duty. Remember, rocks don’t generally melt until you get up around 700 degrees Celsius (over a thousand degrees Fahrenheit). Just making containers that can endure the heat is a challenge. Even more technology is required to ensure that the crystals grow regularly, making the process complicated and expensive.
In general, amateur scientists are best off growing your crystals from solution, and better yet, the chemicals can be bought from a chemical dealer rather than messing around with a rock in the first place. (Who thinks of this stuff?) If you do choose to grow some nice calcite crystals, do take pictures, and send them my way. I’d be interested to see how they turned out.